Permafrost thaw/degradation in the Northern Hemisphere due to global warming is projected to accelerate in coming decades. Assessment of this trend requires improved understanding of the evolution and dynamics of permafrost areas. Land surface models (LSMs) are well-suited for this due to their physical basis and large-scale applicability. However, LSM application is challenging because (a) LSMs demand extensive and accurate meteorological forcing data, which are not readily available for historic conditions and only available with significant biases for future climate, (b) LSMs possess a large number of model parameters, and (c) observations of thermal/hydraulic regimes to constrain those parameters are severely limited. This study addresses these challenges by applying the MESH-CLASS modeling framework (Modélisation Environmenntale communautaire—Surface et Hydrology embedding the Canadian Land Surface Scheme) to three regions within the Mackenzie River Basin, Canada, under various meteorological forcing data sets, using the variogram analysis of response surfaces framework for sensitivity analysis and threshold-based identifiability analysis. The study shows that the modeler may face complex trade-offs when choosing a forcing data set; for current and future scenarios, forcing data require multi-variate bias correction, and some data sets enable the representation of some aspects of permafrost dynamics, but are inadequate for others. The results identify the most influential model parameters and show that permafrost simulation is most sensitive to parameters controlling surface insulation and runoff generation. But the identifiability analysis reveals that many of the most influential parameters are unidentifiable. These conclusions can inform future efforts for data collection and model parameterization.

Abstract. Wetland systems are among the largest stores of carbon on the planet, most biologically diverse of all ecosystems, and dominant controls of the hydrologic cycle. However, their representation in land surface models (LSMs), which are the terrestrial lower boundary of Earth system models (ESMs) that inform climate actions, is limited. Here, we explore different possible parametrizations to represent wetland-groundwater-upland interactions with varying levels of system and computational complexity. We perform a series of numerical experiments that are informed by field observations from wetlands in the well-instrumented White Gull Creek in Saskatchewan, in the boreal region of North America. We show that the typical representation of wetlands in LSMs, which ignores interactions with groundwater and uplands, can be inadequate. We show that the optimal level of model complexity depends on the land cover, soil type, and the ultimate modelling purpose, being nowcasting and prediction, scenario analysis, or diagnostic learning.

Although the temporal transferability of input–output (IO) models has been examined before, no study has investigated the impacts of changing water availability conditions over time, e.g., due to climate change, on the predictive power of water-inclusive IO models. To address this gap, we investigate the performance of inter-regional supply-side input–output (ISIO) models that incorporate precipitation and water intake under varying climates over time in a transboundary water management context. Using the Saskatchewan River Basin in Western Canada as a case study, we develop four ISIO models based on available economic and hydrological data from years with different climatic conditions, i.e., two dry and two wet years. Accounting for price changes over these years, our findings indicate that the joint impact of changes in water availability and economic structural changes on economic output can be considerable. The results furthermore show that each model performs particularly well in predicting the economic output for similar climatic years. The models remain reliable in predicting economic outputs over several years as long as changes in water availability are within the range observed in the water-inclusive base year ISIO model.

Abstract. While conflict-and-cooperation phenomena in transboundary basins have been widely studied, much less work has been devoted to representing the process interactions in a quantitative way. This paper identifies the main factors in the riparian countries' willingness to cooperate in the Eastern Nile River basin, involving Ethiopia, Sudan, and Egypt, from 1983 to 2016. We propose a quantitative model of the willingness to cooperate at the national and river basin scales. Our results suggest that relative political stability and foreign direct investment can explain Ethiopia's decreasing willingness to cooperate between 2009 and 2016. Further, we show that the 2008 food crisis may account for Sudan recovering its willingness to cooperate with Ethiopia. Long-term lack of trust among the riparian countries may have reduced basin-wide cooperation. While the proposed model has some limitations regarding model assumptions and parameters, it does provide a quantitative representation of the evolution of cooperation pathways among the riparian countries, which can be used to explore the effects of changes in future dam operation and other management decisions on the emergence of conflict and cooperation in the basin.

This study proposes a reservoir operation optimization framework to maximize the regional agricultural profit under the constraints of downstream environmental flow requirements and climate change. Three climate change models—CanESM2, MIROC5, and NorESM1-M—and the soil and water assessment tool (SWAT) were used to simulate the reservoir inflow in future periods under uncertainty. Minimum and ideal environmental flow regimes were embedded in the structure of the reservoir operation model to optimize the environmental flow needs and water supply and assess their tradeoffs. Cropping pattern optimization was used to maximize farmer profit. Particle swarm optimization was applied in the optimization processes. The method was applied to a case study in the Tajan River basin, Iran, with the results showing the environmental flow regime considerably reduces irrigation supply and has significant impacts on farmer profits. The results showed that cropping pattern optimization was not an effective strategy to mitigate the economic impacts of climate change under environmental flow constraints, but this assessment may not be generalized to other areas. Uncertainties related to the climate change models are a notable weakness of the approach and should be considered in future studies.

The present study proposes and evaluates an integrated optimization framework for agricultural planning in which an environmental flow model, drought analysis, cropping pattern model, and deficit irrigation functions are linked. Fuzzy physical habitat simulation was used to assess the environmental flow regime. A regression model was applied to develop the deficit irrigation functions. Average river flow time series in three hydrological conditions (dry, normal, and wet) were obtained using drought analysis. The environmental flow model, cropping pattern model, deficit irrigation functions, and river flow time series were then used in the structure of the optimization model. The goal of the optimization model is to provide an agricultural plan, including optimal cropping patterns and irrigation supply that minimizes ecological impacts on the river ecosystem. A genetic algorithm was used in the optimization process. Based on case study results, the proposed model is able to minimize ecological impacts on the river ecosystem in all hydrological conditions and propose an optimal plan for cropping patterns and irrigation supply. The difference between average revenue in the optimal plan and current conditions in all simulated hydrological conditions is less than 10%, which means the optimization system provides a sustainable plan for agricultural and environmental management.

Abstract. Hydrologic-land surface models (H-LSMs) provide physically-based understanding and predictions of the current and future states of the world’s vast high-latitude permafrost regions. Two major challenges, however, hamper their parametrization and validation when concurrently representing hydrology and permafrost. One is the high computational complexity, exacerbated by the need to include a deep soil profile to adequately capture the freeze/thaw cycles and heat storage. The other is that soil-temperature data are severely limited, and traditional model validation, based on streamflow, can show the right fit to these data for the wrong reasons. There are few observational sites for such vast, heterogeneous regions, and remote sensing provides only limited support. In light of these challenges, we develop 16 parametrizations of a Canadian H-LSM, MESH, for the sub-arctic Liard River Basin and validate them using three data sources: streamflows at multiple gauges, soil temperature profiles from few available boreholes, and multiple permafrost maps. The different parametrizations favor different sources of data and it is challenging to configure a model faithful to all three data sources, which are at times inconsistent with each other. Overall, the results show that: (1) surface insulation through snow cover primarily regulates permafrost dynamics after model initialization effects decay over, relatively long time and (2) different parametrizations yield different partitioning patterns of solid-vs-liquid soil-water and produce different low-flow but similar high-flow regimes. We conclude that, given data scarcity, an ensemble of model parametrizations is essential to provide a reliable picture of the current states and future spatio-temporal co-evolution of permafrost and hydrology.

Permafrost plays an important role in the hydrology of arctic/subarctic regions. However, permafrost thaw/degradation has been observed over recent decades in the Northern Hemisphere and is projected to accelerate. Hence, understanding the evolution of permafrost areas is urgently needed. Land surface models (LSMs) are well-suited for predicting permafrost dynamics due to their physical basis and large-scale applicability. However, LSM application is challenging because of the large number of model parameters and the complex memory of state variables. Significant interactions among the underlying processes and the paucity of observations of thermal/hydraulic regimes add further difficulty. This study addresses the challenges of LSM application by evaluating the uncertainty due to meteorological forcing, assessing the sensitivity of simulated permafrost dynamics to LSM parameters, and highlighting issues of parameter identifiability. Modelling experiments are implemented using the MESH-CLASS framework. The VARS sensitivity analysis and traditional threshold-based identifiability analysis are used to assess various aspects of permafrost dynamics for three regions within the Mackenzie River Basin. The study shows that the modeller may face significant trade-offs when choosing a forcing dataset as some datasets enable the representation of some aspects of permafrost dynamics, while being inadequate for others. The results also emphasize the high sensitivity of various aspects of permafrost simulation to parameters controlling surface insulation and soil texture; a detailed list of influential parameters is presented. Identifiability analysis reveals that many of the most influential parameters for permafrost simulation are unidentifiable. These conclusions will hopefully inform future efforts in data collection and model parametrization.

Permafrost thaw has been observed in recent decades in the Northern Hemisphere and is expected to accelerate with continued global warming. Predicting the future of permafrost requires proper representation of the interrelated surface/subsurface thermal and hydrologic regimes. Land surface models (LSMs) are well suited for such predictions, as they couple heat and water interactions across soil-vegetation-atmosphere interfaces and can be applied over large scales. LSMs, however, are challenged by the long-term thermal and hydraulic memories of permafrost and the paucity of historical records to represent permafrost dynamics under transient climate conditions. In this study, we aim to understand better how LSMs function under different spin-up states, which facilitates addressing the challenge of model initialization by characterizing the impact of initial climate conditions and initial soil frozen and liquid water contents on the simulation length required to reach equilibrium. Further, we quantify how the uncertainty in model initialization propagates to simulated permafrost dynamics. Modelling experiments are conducted with the Modélisation Environmentale Communautaire—Surface and Hydrology (MESH) framework and its embedded Canadian land surface scheme (CLASS). The study area is in the Liard River basin in the Northwest Territories of Canada with sporadic and discontinuous regions. Results show that uncertainty in model initialization controls various attributes of simulated permafrost, especially the active layer thickness, which could change by 0.5–1.5 m depending on the initial condition chosen. The least number of spin-up cycles is achieved with near field capacity condition, but the number of cycles varies depending on the spin-up year climate. We advise an extended spin-up of 200–1000 cycles to ensure proper model initialization under different climatic conditions and initial soil moisture contents.

A traditional engineering-based approach to hydro-economic modelling is to connect a partial equilibrium economic assessment, e.g., changes in sectoral production, to a detailed water resources system model. Since the 1990s, another approach emerged where water data are incorporated into a macro-economic model, e.g., a computable general equilibrium or input-output model, to estimate both direct and indirect economic impacts. This study builds on these different approaches and compares the outcomes from three models in the transboundary Saskatchewan River Basin in Canada. The economic impacts of drought and socioeconomic development are estimated using an engineering-based model, a macro-economic model, and a model that integrates a water resources model and a macro-economic model. Findings indicate that although the integrated model is more challenging to develop, its results seem most relevant for water allocation, owing to capturing both regional and sectoral economic interdependencies and key features of the water resources system in more detail. • We compare three hydro-economic modelling approaches in a transboundary river basin. • Their applicability is examined under drought and economic development scenarios. • Usefulness of integrating water management and macroeconomic models is demonstrated. • Ignoring linkages between basins and sectors affects the model simulation results. • This may mislead water allocation decision-making in transboundary river basins.

Cold regions provide water resources for half the global population yet face rapid change. Their hydrology is dominated by snow, ice and frozen soils, and climate warming is having profound effects. Hydrological models have a key role in predicting changing water resources but are challenged in cold regions. Ground-based data to quantify meteorological forcing and constrain model parameterization are limited, while hydrological processes are complex, often controlled by phase change energetics. River flows are impacted by poorly quantified human activities. This paper discusses the scientific and technical challenges of the large-scale modelling of cold region systems and reports recent modelling developments, focussing on MESH, the Canadian community hydrological land surface scheme. New cold region process representations include improved blowing snow transport and sublimation, lateral land-surface flow, prairie pothole pond storage dynamics, frozen ground infiltration and thermodynamics, and improved glacier modelling. New algorithms to represent water management include multistage reservoir operation. Parameterization has been supported by field observations and remotely sensed data; new methods for parameter identification have been used to evaluate model uncertainty and support regionalization. Additionally, MESH has been linked to broader decision-support frameworks, including river ice simulation and hydrological forecasting. The paper also reports various applications to the Saskatchewan and Mackenzie River basins in western Canada (0.4 and 1.8 million km2). These basins arise in glaciated mountain headwaters, are partly underlain by permafrost, and include remote and incompletely understood forested, wetland, agricultural and tundra ecoregions. These illustrate the current capabilities and limitations of cold region modelling, and the extraordinary challenges to prediction, including the need to overcoming biases in forcing data sets, which can have disproportionate effects on the simulated hydrology.

Data-driven hydrological modeling has seen rapid development in recent years owing to its flexibility to approximate the complex relationships between driving forces and hydrological fluxes. However, traditional data-driven models typically cannot simultaneously capture the processes that pose both chronic and acute impacts on streamflow, thus impeding further inference. Therefore, this study presents a baseflow-filtered hydrological inference model to gain insights into hydrological processes in irrigated watersheds. The proposed model starts with separating the streamflow process into two sub-processes using a process-based baseflow separation method. Each sub-process is simulated through a new interpretable data-driven model. The resulting hydrological inferences facilitate the identification of the dominant factors influencing flows in saturated and unsaturated zones. The proposed model is applied to three irrigated watersheds, and the evaluation metrics show that the proposed model outperforms two conventional data-driven models. Our findings reveal that predictors associated with air temperature and long-term (i.e., monthly) irrigation are mainly responsible for characterizing baseflow dynamics, while precipitation and short-term (i.e., semi-weekly or weekly) irrigation are primarily responsible for describing overland flow and interflow dynamics. The fidelity of the derived hydrological inference is further demonstrated through sensitivity analysis. The results show that the relative importance of predictors not only reflects their significance on model performance, but also influence the changes on streamflow.

Abstract Machine learning (ML) applications in Earth and environmental sciences (EES) have gained incredible momentum in recent years. However, these ML applications have largely evolved in ‘isolation’ from the mechanistic, process‐based modelling (PBM) paradigms, which have historically been the cornerstone of scientific discovery and policy support. In this perspective, we assert that the cultural barriers between the ML and PBM communities limit the potential of ML, and even its ‘hybridization’ with PBM, for EES applications. Fundamental, but often ignored, differences between ML and PBM are discussed as well as their strengths and weaknesses in light of three overarching modelling objectives in EES, (1) nowcasting and prediction, (2) scenario analysis, and (3) diagnostic learning. The paper ponders over a ‘coevolutionary’ approach to model building, shifting away from a borrowing to a co‐creation culture, to develop a generation of models that leverage the unique strengths of ML such as scalability to big data and high‐dimensional mapping, while remaining faithful to process‐based knowledge base and principles of model explainability and interpretability, and therefore, falsifiability.

Abstract Machine learning (ML) models have been widely used for hydrological simulation. Previous studies have reported that conventional ML models fail to accurately simulate extreme flows which are crucial for design flood estimation and associated risk analysis in the context of climate change. Therefore, this study proposes a joint probabilistic rainfall‐runoff model (JPRR) for improving high‐to‐extreme flow projection. With the aid of paired copula constructions, bootstrap aggregation, and multi‐model ensemble approaches, the proposed model is able to effectively characterize the dependence relationships of predictors (i.e., precipitation time series with different moving sums) with various probability distributions. JPRR has been applied to four pristine basins in China, representing different climate zones and landscapes. The results reveal that JPRR significantly outperforms three well‐known ML models (i.e., random forest, artificial neural networks, and long short‐term memory) in high‐to‐extreme flow simulations. In JPRR, the copulas exhibiting the right tail dependence play a more important role in streamflow simulations at mountainous basins. Moreover, a significant difference in streamflow projections (from 2030 to 2099) derived from JPRR and benchmark models imply that flood risks from conventional ML models may be underestimated under changing climatic conditions.

Abstract Risk management has reduced vulnerability to floods and droughts globally 1,2 , yet their impacts are still increasing 3 . An improved understanding of the causes of changing impacts is therefore needed, but has been hampered by a lack of empirical data 4,5 . On the basis of a global dataset of 45 pairs of events that occurred within the same area, we show that risk management generally reduces the impacts of floods and droughts but faces difficulties in reducing the impacts of unprecedented events of a magnitude not previously experienced. If the second event was much more hazardous than the first, its impact was almost always higher. This is because management was not designed to deal with such extreme events: for example, they exceeded the design levels of levees and reservoirs. In two success stories, the impact of the second, more hazardous, event was lower, as a result of improved risk management governance and high investment in integrated management. The observed difficulty of managing unprecedented events is alarming, given that more extreme hydrological events are projected owing to climate change 3 .

Abstract The Global Environmental Multiscale Model (GEM) is currently in operational use for data assimilation and forecasting at 25–15 km scales; regional 10 km scales over North America; and 2.5 km scales over Canada. To evaluate the GEM model for forecasting applications in Iran, global daily temperature and precipitation outputs of GEM at a 25 km scale were compared to data sets from hydrometeorological stations and the De Martonne climate classification method was used to demarcate climate zones for comparisons. GEM model outputs were compared to observations in each of these zones. The results show good agreement between GEM outputs and measured daily temperatures with Kling‐Gupta efficiencies of 0.76 for the arid, 0.71 for the semiarid, and 0.78 for the humid regions. There is also an agreement between GEM outputs and measured annual precipitation with differences of 50% for the arid, 36% for the semiarid, and 15% for the humid region. There is a ~13% systematic difference between the elevation of stations and the average elevation of corresponding GEM grid cells; differences in elevation associated with forcing data sets can be potentially corrected using environmental lapse rates. Compared with hydrometeorological data sets, the GEM model precipitation outputs are less accurate than temperature outputs, and this may influence the accuracy of potential Iranian forecasting operations utilizing GEM. The results of this study provide an understanding of the operation and limitations of the GEM model for climate change and hydro‐climatological studies.

Abstract Thermal pollution is an environmental impact of large dams altering the natural temperature regime of downstream river ecosystems. The present study proposes a simulation–optimization framework to reduce thermal pollution downstream from reservoirs and tests it on a real-world case study. This framework attempts to simultaneously minimize the environmental impacts as well as losses to reservoir objectives for water supply. A hybrid machine-learning model is applied to simulate water temperature downstream of the reservoir under various operation scenarios. This model is shown to be robust and achieves acceptable predictive accuracy. The results of simulation–optimization indicate that the reservoir could be operated in such a way that the natural temperature regime is reasonably preserved to protect downstream habitats. Doing so, however, would result in significant trade-offs for reservoir storage and water supply objectives. Such trade-offs can undermine the benefits of reservoirs and need to be carefully considered in reservoir design and operation.

AbstractHydrologic model intercomparison studies help to evaluate the agility of models to simulate variables such as streamflow, evaporation, and soil moisture. This study is the third in a sequen...

Cold regions provide water resources for half the global population yet face rapid change. Their hydrology is dominated by snow, ice and frozen soils, and climate warming is having profound effects. Hydrological models have a key role in predicting changing water resources, but are challenged in cold regions. Ground-based data to quantify meteorological forcing and constrain model parameterization are limited, while hydrological processes are complex, often controlled by phase change energetics. River flows are impacted by poorly quantified human activities. This paper reports scientific developments over the past decade of MESH, the Canadian community hydrological land surface scheme. New cold region process representation includes improved blowing snow transport and sublimation, lateral land-surface flow, prairie pothole storage dynamics, frozen ground infiltration and thermodynamics, and improved glacier modelling. New algorithms to represent water management include multi-stage reservoir operation. Parameterization has been supported by field observations and remotely sensed data; new methods for parameter identification have been used to evaluate model uncertainty and support regionalization. Additionally, MESH has been linked to broader decision-support frameworks, including river ice simulation and hydrological forecasting. The paper also reports various applications to the Saskatchewan and Mackenzie River basins in western Canada (0.4 and 1.8 million km). These basins arise in glaciated mountain headwaters, are partly underlain by permafrost, and include remote and incompletely understood forested, wetland, agricultural and tundra ecoregions. This imposes extraordinary challenges to prediction, including the need to overcoming biases in forcing data sets, which can have disproportionate effects on the simulated hydrology.

Recent breakthroughs in artificial intelligence (AI), and particularly in deep learning (DL), have created tremendous excitement and opportunities in the earth and environmental sciences communities. To leverage these new ‘data-driven’ technologies, however, one needs to understand the fundamental concepts that give rise to DL and how they differ from ‘process-based’, mechanistic modelling. This paper revisits those fundamentals and addresses 10 questions often posed by earth and environmental scientists with the aid of a real-world modelling experiment. The overarching objective is to contribute to a future of AI-assisted earth and environmental sciences where DL models can (1) embrace the typically ignored knowledge base available, (2) function credibly in ‘true’ out-of-sample prediction, and (3) handle non-stationarity in earth and environmental systems. Comparing and contrasting earth and environmental problems with prominent AI applications, such as playing chess and trading in stock markets, provides critical insights for better directing future research in this field.

In this study, we develop a hydro-economic modelling framework for river-basin scales by integrating a water resources system model and an economic model. This framework allows for the representation of both local-scale features, such as reservoirs, diversions, and water licenses and priorities, and regional- and provincial-scale features, such as cross-sectoral and inter-regional connectedness and trade flows. This framework is able to: (a) represent nonlinearities and interactions that cannot be represented by either of typical water resources or economic models; (b) analyze the sensitivity of macro-scale economy to different local water management decisions (called 'decision levers' herein); and (c) identify water allocation strategies that are economically sound across sectors and regions. This integrated model is applied to the multi-jurisdictional Saskatchewan River Basin in Western Canada. Our findings reveal that an economically optimal water allocation strategy can mitigate the economic losses of water stress up to 80% compared to the existing water allocation strategy. We draw lessons from our analysis and discuss how integrated inter-regional hydro-economic modelling can benefit vulnerability assessment and robust decision making.

The farmers in the Bow River Basin (BRB), Canada, have adopted water conservation strategies to reduce water needs. This reduction, however, encouraged irrigation expansion, which may rebound agric...

• Time-varying GSA offers a good understanding of the coupled human-natural systems. • Economy is the most influential factor in the rebound phenomenon of the BRB. • Social interaction had a high total-effect on the rebound phenomenon of the BRB. • Raising farmers’ awareness by formal channels could avoid the rebound phenomenon. • Switching to crops needing less water could prevent the rebound phenomenon. Modernizing traditional irrigation systems has long been recognized as a means to reduce water losses. However, empirical evidence shows that this practice may not necessarily reduce water use in the long run; in fact, in many cases, the converse is true—a concept known as the rebound phenomenon. This phenomenon is at the heart of a fundamental research gap in the explicit evaluation of co-evolutionary dynamics and interactions among socio-economic and hydrologic factors in agricultural systems. This gap calls for the application of systems-based methods to evaluate such dynamics. To address this gap, we use a previously developed Agent-Based Agricultural Water Demand (ABAD) model, applied to the Bow River Basin (BRB) in Canada. We perform a time-varying variance-based global sensitivity analysis (GSA) on the ABAD model to examine the individual effect of factors, as well as their joint effect, that may give rise to the rebound phenomenon in the BRB. Our results show that economic factors dominantly control possible rebounds. Although social interaction among farmers is found to be less influential than the irrigation expansion factor, its interaction effect with other factors becomes more important, indicating the highly interactive nature of the underlying socio-hydrological system. Based on the insights gained via GSA, we discuss several strategies, including community participation and water restrictions, that can be adopted to avoid the rebound phenomenon in irrigation systems. This study demonstrates that a time-varying variance-based GSA can provide a better understanding of the co-evolutionary dynamics of the socio-hydrological systems and can pave the way for better management of water resources.

Sensitivity analysis (SA) is en route to becoming an integral part of mathematical modeling. The tremendous potential benefits of SA are, however, yet to be fully realized, both for advancing mechanistic and data-driven modeling of human and natural systems, and in support of decision making. In this perspective paper, a multidisciplinary group of researchers and practitioners revisit the current status of SA, and outline research challenges in regard to both theoretical frameworks and their applications to solve real-world problems. Six areas are discussed that warrant further attention, including (1) structuring and standardizing SA as a discipline, (2) realizing the untapped potential of SA for systems modeling, (3) addressing the computational burden of SA, (4) progressing SA in the context of machine learning, (5) clarifying the relationship and role of SA to uncertainty quantification, and (6) evolving the use of SA in support of decision making. An outlook for the future of SA is provided that underlines how SA must underpin a wide variety of activities to better serve science and society. • Sensitivity analysis (SA) should be promoted as an independent discipline. • Several grand challenges hinder full realization of the benefits of SA. • The potential of SA for systems modeling & machine learning is untapped. • New prospects exist for SA to support uncertainty quantification & decision making. • Coordination rather than consensus is key to cross-fertilize new ideas.

Sensitivity analysis (SA) as a ‘formal’ and ‘standard’ component of scientific development and policy support is relatively young. Many researchers and practitioners from a wide range of disciplines have contributed to SA over the last three decades, and the SAMO (sensitivity analysis of model output) conferences, since 1995, have been the primary driver of breeding a community culture in this heterogeneous population. Now, SA is evolving into a mature and independent field of science, indeed a discipline with emerging applications extending well into new areas such as data science and machine learning. At this growth stage, the present editorial leads a special issue consisting of one Position Paper on “ The future of sensitivity analysis ” and 11 research papers on “ Sensitivity analysis for environmental modelling ” published in Environmental Modelling & Software in 2020–21. • Advances of science and policy has deep but informal roots in sensitivity analysis. • Modern sensitivity analysis is now evolving into a formal and independent discipline. • New areas such data science and machine learning benefit from sensitivity analysis. • Challenges, methodological progress, and outlook are outlined in this special issue.

Abstract. The interior of western Canada, like many similar cold mid- to high-latitude regions worldwide, is undergoing extensive and rapid climate and environmental change, which may accelerate in the coming decades. Understanding and predicting changes in coupled climate–land–hydrological systems are crucial to society yet limited by lack of understanding of changes in cold-region process responses and interactions, along with their representation in most current-generation land-surface and hydrological models. It is essential to consider the underlying processes and base predictive models on the proper physics, especially under conditions of non-stationarity where the past is no longer a reliable guide to the future and system trajectories can be unexpected. These challenges were forefront in the recently completed Changing Cold Regions Network (CCRN), which assembled and focused a wide range of multi-disciplinary expertise to improve the understanding, diagnosis, and prediction of change over the cold interior of western Canada. CCRN advanced knowledge of fundamental cold-region ecological and hydrological processes through observation and experimentation across a network of highly instrumented research basins and other sites. Significant efforts were made to improve the functionality and process representation, based on this improved understanding, within the fine-scale Cold Regions Hydrological Modelling (CRHM) platform and the large-scale Modélisation Environmentale Communautaire (MEC) – Surface and Hydrology (MESH) model. These models were, and continue to be, applied under past and projected future climates and under current and expected future land and vegetation cover configurations to diagnose historical change and predict possible future hydrological responses. This second of two articles synthesizes the nature and understanding of cold-region processes and Earth system responses to future climate, as advanced by CCRN. These include changing precipitation and moisture feedbacks to the atmosphere; altered snow regimes, changing balance of snowfall and rainfall, and glacier loss; vegetation responses to climate and the loss of ecosystem resilience to wildfire and disturbance; thawing permafrost and its influence on landscapes and hydrology; groundwater storage and cycling and its connections to surface water; and stream and river discharge as influenced by the various drivers of hydrological change. Collective insights, expert elicitation, and model application are used to provide a synthesis of this change over the CCRN region for the late 21st century.

System-of-systems approaches for integrated assessments have become prevalent in recent years. Such approaches integrate a variety of models from different disciplines and modeling paradigms to represent a socio-environmental (or social-ecological) system aiming to holistically inform policy and decision-making processes. Central to the system-of-systems approaches is the representation of systems in a multi-tier framework with nested scales. Current modeling paradigms, however, have disciplinary-specific lineage, leading to inconsistencies in the conceptualization and integration of socio-environmental systems. In this paper, a multidisciplinary team of researchers, from engineering, natural and social sciences, have come together to detail socio-technical practices and challenges that arise in the consideration of scale throughout the socio-environmental modeling process. We identify key paths forward, focused on explicit consideration of scale and uncertainty, strengthening interdisciplinary communication, and improvement of the documentation process. We call for a grand vision (and commensurate funding) for holistic system-of-systems research that engages researchers, stakeholders, and policy makers in a multi-tiered process for the co-creation of knowledge and solutions to major socio-environmental problems.

• The choice of energy-balance or temperature-index snowmelt modules is often ad-hoc. • Two snowmelt modules under two snow density functions are examined in SWAT model. • Cascade of uncertainty for future projections varies across spatiotemporal scales. • Snow density approach is a major control of snow depth simulation and projection. • Unlike mountains, in plain, snowmelt module uncertainties are scanty but vary in time. Snowmelt is a major driver of the hydrological cycle in cold regions, as such, its accurate representation in hydrological models is key to both regional snow depth and streamflow prediction. The choice of a proper method for snowmelt representation is often improvised; however, a thorough characterization of uncertainty in such process representations particularly in the context of climate change has remained essential. To fill this gap, this study revisits and characterizes performance and uncertainty around the two general approaches to snowmelt representation, namely Energy-Balance Modules (EBMs) and Temperature-Index Modules (TIMs). To account for snow depth simulation and projection, two common Snow Density formulations (SNDs) are implemented that map snow water equivalent (SWE) to snow depth. The major research questions we address are two-fold. First, we examine the dominant controls of uncertainty in snow depth and streamflow simulations across scales and in different climates. Second, we evaluate the cascade of uncertainty of snow depth projections resulting from impact model parameters, greenhouse gas emission scenarios, climate models and their internal variability, and downscaling processes. We enable the Soil and Water Assessment Tool (SWAT) by coupling EBM, TIM, and two SND modules for examination of different snowmelt representation methods, and Analysis of Variance (ANOVA) for uncertainty decomposition and attribution. These analyses are implemented in mountainous, foothill, and plain regions in a large snow-dominated watershed in western Canada. Results show, rather counter-intuitively, that the choice of SND is a major control of performance and uncertainty of snow depth simulation rather than the choice between TIMs and EBMs and of their uncertain parameters. Also, analysis of streamflow simulations suggest that EBMs generally overestimate streamflow on main tributaries. Finally, uncertainty decompositions show that parameter uncertainty related to snowmelt modules dominantly controls uncertainty in future snow depth projections under climate change, particularly in mountainous regions. However, in plain regions, the uncertainty contribution of model parameters becomes more variable with time and less dominant compared with the other sources of uncertainty. Overall, it is shown that the hydro-climatic and topographic conditions of different regions, as well as input data availability, have considerable effect on reproduction of snow depth, snowmelt and resulting streamflow, and on the share of different uncertainty sources when projecting regional snow depth.

• Simulation-optimization techniques are essential but computationally cumbersome. • Classic surrogates that globally emulate response surfaces can be of limited help. • Local surrogate models are proposed using automatic clustering for simulation. • The proposed method is shown to be efficient and robust in groundwater remediation. Simulation-optimization techniques in support of groundwater management are computationally expensive. To tackle such computational burden, a variety of surrogate modeling-frameworks have been proposed, where a cheaper-to-run model referred to as a surrogate is used in lieu of a computationally intensive model. These frameworks are generally based on what referred herein to as ‘global surrogate modelling’ where a single surrogate approximates the underlying response surface of a model. Such classic frameworks, however, are sub-optimal when the response surface is complex and/or high-dimensional. This paper proposes a novel ‘local surrogate modelling’ framework that simultaneously builds and evolves multiple local surrogates, guided by an automatic clustering method. Unlike traditional clustering methods that select the number of clusters a priori, the proposed automatic clustering method concurrently determines the optimum number of clusters and the clustering scheme itself. To serve as the surrogate, Artificial Neural Networks (ANNs) are used. The proposed framework is applied to solve a computationally intensive groundwater remediation optimization problem. This study shows that the proposed automatic clustering-based local surrogate modeling is effective and reliable while reducing at least 60 percent of the computational burden.

• Time-variant variogram analysis reveals significant event scale parameter importance variability. • The type of modeling objectives used influences parameter importance. • Input rainfall intensity and hyetograph shape affects parameters importance. • VARS is an effective and robust approach for identifying key modeling parameters. Runoff and sediment yield predictions using rainfall-runoff modeling systems play a significant role in developing sustainable rangeland and water resource management strategies. To characterize the behavior and predictive uncertainty of the KINEROS2 physically-based distributed hydrologic model, we assessed model parameters importance at the event-scale for small nested semi-arid subwatersheds in southeastern Arizona using the Variogram Analysis of Response Surfaces (VARS) methodology. A two-pronged approach using time-aggregate and time-variant parameter importance analysis was adopted to improve understanding of the control and behavior of models. The time-aggregate analysis looks at several signature responses, including runoff volume, sediment yield, peak runoff, runoff duration, time to peak, lag time, and recession duration, to investigate the influence of parameter and input on the model predictions. The time-variant analysis looks at the dynamical influence of parameters on the simulation of flow and sediment rates at every simulation time step using the different forcing inputs. This investigation was able to address Simpson’s paradox-type issues where the analysis across the different objective functions and full data set vs. its subsets (i.e., different events and/or time steps) could yield inconsistent and potentially misleading results. The results indicated the uncertainties in the flow responses are primarily due to the saturated hydraulic conductivity, the Manning’s coefficient, the soil capillary coefficient, and the cohesion in sediment and flow-related responses. The level of influence of K2 parameters depends on the type of the model response surface, the rainfall, and the watershed size.

• Development of the ensemble-based data assimilation framework is examined. • GRACE assimilation improves the simulation of snow estimates at the basin and grid scales. • Data assimilation can effectively constrain the amplitude of modeled water storage dynamics. • GRACE data assimilation improves the simulation of high flows during snowmelt season. Accurate estimation of snow mass or snow water equivalent (SWE) over space and time is required for global and regional predictions of the effects of climate change. This work investigates whether integration of remotely sensed terrestrial water storage (TWS) information, which is derived from the Gravity Recovery and Climate Experiment (GRACE), can improve SWE and streamflow simulations within a semi-distributed hydrology land surface model. A data assimilation (DA) framework was developed to combine TWS observations with the MESH (Modélisation Environnementale Communautaire – Surface Hydrology) model using an ensemble Kalman smoother (EnKS). The snow-dominated Liard Basin was selected as a case study. The proposed assimilation methodology reduced bias of monthly SWE simulations at the basin scale by 17.5% and improved unbiased root-mean-square difference (ubRMSD) by 23%. At the grid scale, the DA method improved ubRMSD values and correlation coefficients for 85% and 97% of the grid cells, respectively. Effects of GRACE DA on streamflow simulations were evaluated against observations from three river gauges, where it effectively improved the simulation of high flows during snowmelt season from April to June. The influence of GRACE DA on the total flow volume and low flows was found to be variable. In general, the use of GRACE observations in the assimilation framework not only improved the simulation of SWE, but also effectively influenced streamflow simulations.

Abstract. The assumption of stationarity in water resources no longer holds, particularly within the context of future climate change. Plausible scenarios of flows that fluctuate outside the envelope of variability of the gauging data are required to assess the robustness of water resource systems to future conditions. This study presents a novel method of generating weekly time step flows based on tree-ring chronology data. Specifically, this method addresses two long-standing challenges with paleo-reconstruction: (i) the typically limited predictive power of tree-ring data at the annual and sub-annual scale and (ii) the inflated short-term persistence in tree-ring time series and improper use of pre-whitening. Unlike the conventional approach, this method establishes relationships between tree-ring chronologies and naturalized flow at a biennial scale to preserve persistence properties and variability of hydrological time series. Biennial flow reconstructions are further disaggregated to weekly flow reconstructions, according to the weekly flow distribution of reference 2-year instrumental periods, identified as periods with broadly similar tree-ring properties to those of every 2-year paleo-period. The Saskatchewan River basin (SaskRB) in Western Canada is selected as a study area, and weekly flows in its four major tributaries are extended back to the year 1600. The study shows that the reconstructed flows properly preserve the statistical properties of the reference flows, particularly in terms of short- to long-term persistence and the structure of variability across timescales. An ensemble approach is presented to represent the uncertainty inherent in the statistical relationships and disaggregation method. The ensemble of reconstructed weekly flows are publicly available for download from https://doi.org/10.20383/101.0139 (Slaughter and Razavi, 2019).

Global Institute for Water Security, School of Environment and Sustainability, Department of Civil, Geological, and Environmental Engineering, University of Saskatchewan, Saskatoon, Saskatchewan, Canada School of Geographical Sciences and Urban Planning, Arizona State University, Tempe, Arizona School of Civil, Environmental and Mining Engineering, University of Adelaide, Adelaide, Australia Water Institute and Department of Economics, University of Waterloo, Waterloo, Ontario, Canada Institute for Environmental Studies, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands Department of Civil and Environmental Engineering, Imperial College London, London, UK

Global sensitivity analysis (GSA) provides essential insights into the behavior of Earth and environmental systems models and identifies dominant controls of output uncertainty. Previous work on GSA, however, has typically been under the assumption that the controlling factors such as model inputs and parameters are independent, whereas, in many cases, they are correlated and their joint distribution follows a variety of forms. Although this assumption can limit the credibility of GSA and its results, very few studies in the field of water and environmental modeling address this issue. In this paper, we first discuss the significance of correlation effects in GSA and then propose a new GSA framework for properly accounting for correlations in input/parameter spaces. To this end, we extend the “variogram‐based” theory of GSA, called variogram analysis of response surfaces (VARS), and develop a new generalized star sampling technique (called gSTAR) to accommodate correlated multivariate distributions. We test the new gSTAR‐VARS method on two test functions, against a state‐of‐the‐art GSA method that handles correlation effects. We then apply gSTAR‐VARS to the HBV‐SASK model, calibrated via a Bayesian, Markov chain Monte Carlo approach, for design flood estimation in the Oldman River Basin in Canada. Results demonstrate that accounting for correlation effects can be critically important in GSA, especially in the presence of nonlinearity and interaction effects in the underlying response surfaces. The proposed method can efficiently handle correlations and different distribution types and simultaneously generate a range of sensitivity indices, such as total‐variogram effects, variance‐based total‐order effects, and derivative‐based elementary effects.

Finding sustainable pathways to efficiently allocate limited available water resources among increasingly competing water uses has become crucial due to climate-change-induced water shortages and increasing water demand. This has led to an urgent need for the inclusion of economic principles, models, and methods in water resources management. Although several studies have developed macro-economic models to evaluate the economic impacts of alternative water allocation strategies, many if not most ignore the hydrological boundaries of transboundary river basins. Furthermore, of those using input-output (IO) models, only a handful have applied supply-side IO models. In this paper, we present one of the first attempts to develop an inter-regional, supply-side IO modelling framework for a multi-jurisdictional, transboundary river basin to assess the direct and indirect economic impacts of water supply restrictions due to climate and policy change. Applying this framework to the Saskatchewan River Basin in Canada encompassing three provinces, we investigate the economic impacts of two different water supply restriction scenarios on the entire river basin and its sub-basins individually. We find that in the face of climate-change-induced water shortage, economic losses can be reduced by almost 50% by adopting appropriate management practices, including prioritization of water allocation, using alternative water sources, and water re-use technologies. • Sectoral water use is incorporated into a supply-side input-output model. • The model is spatially disaggregated into 6 sub-basins across 3 Canadian provinces. • The model evaluates the economic impacts of alternative water allocation policies. • The model results assist policymakers prepare efficient water management plans. • Adopting proper policies, potential economic drought losses can be reduced by 50%.

Abstract. Permafrost is an important feature of cold-region hydrology, particularly in river basins such as the Mackenzie River basin (MRB), and it needs to be properly represented in hydrological and land surface models (H-LSMs) built into existing Earth system models (ESMs), especially under the unprecedented climate warming trends that have been observed. Higher rates of warming have been reported in high latitudes compared to the global average, resulting in permafrost thaw with wide-ranging implications for hydrology and feedbacks to climate. The current generation of H-LSMs is being improved to simulate permafrost dynamics by allowing deep soil profiles and incorporating organic soils explicitly. Deeper soil profiles have larger hydraulic and thermal memories that require more effort to initialize. This study aims to devise a robust, yet computationally efficient, initialization and parameterization approach applicable to regions where data are scarce and simulations typically require large computational resources. The study further demonstrates an upscaling approach to inform large-scale ESM simulations based on the insights gained by modelling at small scales. We used permafrost observations from three sites along the Mackenzie River valley spanning different permafrost classes to test the validity of the approach. Results show generally good performance in reproducing present-climate permafrost properties at the three sites. The results also emphasize the sensitivity of the simulations to the soil layering scheme used, the depth to bedrock, and the organic soil properties.

Sensitivity analysis in Earth and environmental systems modeling typically demands an onerous computational cost. This issue coexists with the reliance of these algorithms on ad hoc designs of experiments, which hampers making the most out of the existing data sets. We tackle this problem by introducing a method for sensitivity analysis, based on the theory of variogram analysis of response surfaces (VARS), that works on any sample of input-output data or pre-computed model evaluations. Called data-driven VARS (D-VARS), this method characterizes the relationship strength between inputs and outputs by investigating their covariograms. We also propose a method to assess “robustness” of the results against sampling variability and numerical methods' imperfectness. Using two hydrologic modeling case studies, we show that D-VARS is highly efficient and statistically robust, even when the sample size is small. Therefore, D-VARS can provide unique opportunities to investigate geophysical systems whose models are computationally expensive or available data is scarce.

Abstract Global gridded precipitation products have proven essential for many applications ranging from hydrological modeling and climate model validation to natural hazard risk assessment. They provide a global picture of how precipitation varies across time and space, specifically in regions where ground-based observations are scarce. While the application of global precipitation products has become widespread, there is limited knowledge on how well these products represent the magnitude and frequency of extreme precipitation—the key features in triggering flood hazards. Here, five global precipitation datasets (MSWEP, CFSR, CPC, PERSIANN-CDR, and WFDEI) are compared to each other and to surface observations. The spatial variability of relatively high precipitation events (tail heaviness) and the resulting discrepancy among datasets in the predicted precipitation return levels were evaluated for the time period 1979–2017. The analysis shows that 1) these products do not provide a consistent representation of the behavior of extremes as quantified by the tail heaviness, 2) there is strong spatial variability in the tail index, 3) the spatial patterns of the tail heaviness generally match the Köppen–Geiger climate classification, and 4) the predicted return levels for 100 and 1000 years differ significantly among the gridded products. More generally, our findings reveal shortcomings of global precipitation products in representing extremes and highlight that there is no single global product that performs best for all regions and climates.

Abstract. Hydrologic-Land Surface Models (H-LSMs) have been progressively developed to a stage where they represent the dominant hydrological processes for a variety of hydrological regimes and include a range of water management practices, and are increasingly used to simulate water storages and fluxes of large basins under changing environmental conditions across the globe. However, efforts for comprehensive evaluation of the utility of H-LSMs in large, regulated watersheds have been limited. In this study, we evaluated the capability of a Canadian H-LSM, called MESH, in the highly regulated Saskatchewan River Basin (SaskRB), Canada, under the constraint of significant precipitation uncertainty. The SaskRB is a complex system characterized by hydrologically-distinct regions that include the Rocky Mountains, Boreal Forest, and the Prairies. This basin is highly vulnerable to potential climate change and extreme events. A comprehensive analysis of the MESH model performance was carried out in two steps. First, the reliability of multiple precipitation products was evaluated against climate station observations and based on their performance in simulating streamflow across the basin when forcing the MESH model with a default parameterization. Second, a state-of-the-art multi-criteria calibration approach was applied, using various observational information including streamflow, storage and fluxes for calibration and validation. The first analysis shows that the quality of precipitation products had a direct and immediate impact on simulation performance for the basin headwaters but effects were dampened when going downstream. In particular, the Canadian Precipitation Analysis (CaPA) performed the best among the precipitation products in capturing timings and minimizing the magnitude of error against observation, despite a general underestimation of precipitation amount. The subsequent analyses show that the MESH model was able to capture observed responses of multiple fluxes and storage across the basin using a global multi-station calibration method. Despite poorer performance in some basins, the global parameterization generally achieved better model performance than a default model parameterization. Validation using storage anomaly and evapotranspiration generally showed strong correlation with observations, but revealed potential deficiencies in the simulation of storage anomaly over open water areas.

Abstract. Complex, software-intensive, technically advanced, and computationally demanding models, presumably with ever-growing realism and fidelity, have been widely used to simulate and predict the dynamics of the Earth and environmental systems. The parameter-induced simulation crash (failure) problem is typical across most of these models, despite considerable efforts that modellers have directed at model development and implementation over the last few decades. A simulation failure mainly occurs due to the violation of the numerical stability conditions, non-robust numerical implementations, or errors in programming. However, the existing sampling-based analysis techniques such as global sensitivity analysis (GSA) methods, which require running these models under many configurations of parameter values, are ill-equipped to effectively deal with model failures. To tackle this problem, we propose a novel approach that allows users to cope with failed designs (samples) during the GSA, without knowing where they took place and without re-running the entire experiment. This approach deems model crashes as missing data and uses strategies such as median substitution, single nearest neighbour, or response surface modelling to fill in for model crashes. We test the proposed approach on a 10-paramter HBV-SASK rainfall-runoff model and a 111-parameter MESH land surface-hydrology model. Our results show that response surface modelling is a superior strategy, out of the data filling strategies tested, and can scale well to the dimensionality of the model, sample size, and the ratio of number of failures to the sample size. Further, we conduct a "failure analysis" and discuss some possible causes of the MESH model failure.

Abstract. Reservoirs significantly affect flow regimes in watershed systems by changing the magnitude and timing of streamflows. Failure to represent these effects limits the performance of hydrological and land surface models (H-LSMs) in the many highly regulated basins across the globe and limits the applicability of such models to investigate the futures of watershed systems through scenario analysis (e.g., scenarios of climate, land use, or reservoir regulation changes). An adequate representation of reservoirs and their operation in an H-LSM is therefore essential for a realistic representation of the downstream flow regime. In this paper, we present a general parametric reservoir operation model based on piecewise linear relationships between reservoir storage, inflow, and release, to approximate actual reservoir operations. For the identification of the model parameters, we propose two strategies: (a) a generalized parameterization that requires a relatively limited amount of data; and (b) direct calibration via multi-objective optimization when more data on historical storage and release are available. We use data from 37 reservoir case studies located in several regions across the globe for developing and testing the model. We further build this reservoir operation model into the MESH modelling system, which is a large-scale H-LSM. Our results across the case studies show that the proposed reservoir model with both of the parameter identification strategies leads to improved simulation accuracy compared with the other widely used approaches for reservoir operation simulation. We further show the significance of enabling MESH with this reservoir model and discuss the interdependent effects of the simulation accuracy of natural processes and that of reservoir operation on the overall model performance. The reservoir operation model is generic and can be integrated into any H-LSM.

Abstract. Reservoirs significantly affect flow regimes in watershed systems by changing the magnitude and timing of streamflows. Failure to represent these effects limits the performance of hydrological and land-surface models (H-LSMs) in the many highly regulated basins across the globe and limits the applicability of such models to investigate the futures of watershed systems through scenario analysis (e.g., scenarios of climate, land use, or reservoir regulation changes). An adequate representation of reservoirs and their operation in an H-LSM is therefore essential for a realistic representation of the downstream flow regime. In this paper, we present a general parametric reservoir operation model based on piecewise-linear relationships between reservoir storage, inflow, and release to approximate actual reservoir operations. For the identification of the model parameters, we propose two strategies: (a) a “generalized” parameterization that requires a relatively limited amount of data and (b) direct calibration via multi-objective optimization when more data on historical storage and release are available. We use data from 37 reservoir case studies located in several regions across the globe for developing and testing the model. We further build this reservoir operation model into the MESH (Modélisation Environmentale-Surface et Hydrologie) modeling system, which is a large-scale H-LSM. Our results across the case studies show that the proposed reservoir model with both parameter-identification strategies leads to improved simulation accuracy compared with the other widely used approaches for reservoir operation simulation. We further show the significance of enabling MESH with this reservoir model and discuss the interdependent effects of the simulation accuracy of natural processes and that of reservoir operations on the overall model performance. The reservoir operation model is generic and can be integrated into any H-LSM.

Identifiability is a fundamental concept in parameter estimation, and therefore key to the large majority of environmental modeling applications. Parameter identifiability analysis assesses whether it is theoretically possible to estimate unique parameter values from data, given the quantities measured, conditions present in the forcing data, model structure (and objective function), and properties of errors in the model and observations. In other words, it tackles the problem of whether the right type of data is available to estimate the desired parameter values. Identifiability analysis is therefore an essential technique that should be adopted more routinely in practice, alongside complementary methods such as uncertainty analysis and evaluation of model performance. This article provides an introductory overview to the topic. We recommend that any modeling study should document whether a model is non-identifiable, the source of potential non-identifiability, and how this affects intended project outcomes.

Environmental models are used extensively to evaluate the effectiveness of a range of design, planning, operational, management and policy options. However, the number of options that can be evaluated manually is generally limited, making it difficult to identify the most suitable options to consider in decision-making processes. By linking environmental models with evolutionary and other metaheuristic optimization algorithms, the decision options that make best use of scarce resources, achieve the best environmental outcomes for a given budget or provide the best trade-offs between competing objectives can be identified. This Introductory Overview presents reasons for embedding formal optimization approaches in environmental decision-making processes, details how environmental problems are formulated as optimization problems and outlines how single- and multi-objective optimization approaches find good solutions to environmental problems. Practical guidance and potential challenges are also provided.

Abstract Many applications of global sensitivity analysis (GSA) do not adequately account for the dynamical nature of earth and environmental systems models. Gupta and Razavi (2018) highlight this fact and develop a sensitivity analysis framework from first principles, based on the sensitivity information contained in trajectories of partial derivatives of the dynamical model responses with respect to controlling factors. Here, we extend and generalize that framework to accommodate any GSA philosophy, including derivative-based approaches (such as Morris and DELSA), direct-response-based approaches (such as the variance-based Sobol’, distribution-based PAWN, and higher-moment-based methods), and unifying variogram-based approaches (such as VARS). The framework is implemented within the VARS-TOOL software toolbox and demonstrated using the HBV-SASK model applied to the Oldman Watershed, Canada. This enables a comprehensive multi-variate investigation of the influence of parameters and forcings on different modeled state variables and responses, without the need for observational data regarding those responses.

Abstract VARS-TOOL is a software toolbox for sensitivity and uncertainty analysis. Developed primarily around the “Variogram Analysis of Response Surfaces” framework, VARS-TOOL adopts a multi-method approach that enables simultaneous generation of a range of sensitivity indices, including ones based on derivative, variance, and variogram concepts, from a single sample. Other special features of VARS-TOOL include (1) novel tools for time-varying and time-aggregate sensitivity analysis of dynamical systems models, (2) highly efficient sampling techniques, such as Progressive Latin Hypercube Sampling (PLHS), that maximize robustness and rapid convergence to stable sensitivity estimates, (3) factor grouping for dealing with high-dimensional problems, (4) visualization for monitoring stability and convergence, (5) model emulation for handling model crashes, and (6) an interface that allows working with any model in any programming language and operating system. As a test bed for training and research, VARS-TOOL provides a set of mathematical test functions and the (dynamical) HBV-SASK hydrologic model.

Abstract. Complex, software-intensive, technically advanced, and computationally demanding models, presumably with ever-growing realism and fidelity, have been widely used to simulate and predict the dynamics of the Earth and environmental systems. The parameter-induced simulation crash (failure) problem is typical across most of these models despite considerable efforts that modellers have directed at model development and implementation over the last few decades. A simulation failure mainly occurs due to the violation of numerical stability conditions, non-robust numerical implementations, or errors in programming. However, the existing sampling-based analysis techniques such as global sensitivity analysis (GSA) methods, which require running these models under many configurations of parameter values, are ill equipped to effectively deal with model failures. To tackle this problem, we propose a new approach that allows users to cope with failed designs (samples) when performing GSA without rerunning the entire experiment. This approach deems model crashes as missing data and uses strategies such as median substitution, single nearest-neighbor, or response surface modeling to fill in for model crashes. We test the proposed approach on a 10-parameter HBV-SASK (Hydrologiska Byråns Vattenbalansavdelning modified by the second author for educational purposes) rainfall–runoff model and a 111-parameter Modélisation Environmentale–Surface et Hydrologie (MESH) land surface–hydrology model. Our results show that response surface modeling is a superior strategy, out of the data-filling strategies tested, and can comply with the dimensionality of the model, sample size, and the ratio of the number of failures to the sample size. Further, we conduct a “failure analysis” and discuss some possible causes of the MESH model failure that can be used for future model improvement.

Abstract Dynamical earth and environmental systems models are typically computationally intensive and highly parameterized with many uncertain parameters. Together, these characteristics severely limit the applicability of Global Sensitivity Analysis (GSA) to high-dimensional models because very large numbers of model runs are typically required to achieve convergence and provide a robust assessment. Paradoxically, only 30 percent of GSA applications in the environmental modelling literature have investigated models with more than 20 parameters, suggesting that GSA is under-utilized on problems for which it should prove most useful. We develop a novel grouping strategy, based on bootstrap-based clustering, that enables efficient application of GSA to high-dimensional models. We also provide a new measure of robustness that assesses GSA stability and convergence. For two models, having 50 and 111 parameters, we show that grouping-enabled GSA provides results that are highly robust to sampling variability, while converging with a much smaller number of model runs.

Abstract. Drought is a recurring extreme climate event and among the most costly natural disasters in the world. This is particularly true over Canada, where drought is both a frequent and damaging phenomenon with impacts on regional water resources, agriculture, industry, aquatic ecosystems, and health. However, nationwide drought assessments are currently lacking and impacted by limited ground-based observations. This study provides a comprehensive analysis of historical droughts over the whole of Canada, including the role of large-scale teleconnections. Drought events are characterized by the Standardized Precipitation Evapotranspiration Index (SPEI) over various temporal scales (1, 3, 6, and 12 consecutive months, 6 months from April to September, and 12 months from October to September) applied to different gridded monthly data sets for the period 1950–2013. The Mann–Kendall test, rotated empirical orthogonal function, continuous wavelet transform, and wavelet coherence analyses are used, respectively, to investigate the trend, spatio-temporal patterns, periodicity, and teleconnectivity of drought events. Results indicate that southern (northern) parts of the country experienced significant trends towards drier (wetter) conditions although substantial variability exists. Two spatially well-defined regions with different temporal evolution of droughts were identified – the Canadian Prairies and northern central Canada. The analyses also revealed the presence of a dominant periodicity of between 8 and 32 months in the Prairie region and between 8 and 40 months in the northern central region. These cycles of low-frequency variability are found to be associated principally with the Pacific–North American (PNA) and Multivariate El Niño/Southern Oscillation Index (MEI) relative to other considered large-scale climate indices. This study is the first of its kind to identify dominant periodicities in drought variability over the whole of Canada in terms of when the drought events occur, their duration, and how often they occur.

Abstract. Arctic and subarctic regions are amongst the most susceptible regions on Earth to global warming and climate change. Understanding and predicting the impact of climate change in these regions require a proper process representation of the interactions between climate, carbon cycle, and hydrology in Earth system models. This study focuses on land surface models (LSMs) that represent the lower boundary condition of general circulation models (GCMs) and regional climate models (RCMs), which simulate climate change evolution at the global and regional scales, respectively. LSMs typically utilize a standard soil configuration with a depth of no more than 4 m, whereas for cold, permafrost regions, field experiments show that attention to deep soil profiles is needed to understand and close the water and energy balances, which are tightly coupled through the phase change. To address this gap, we design and run a series of model experiments with a one-dimensional LSM, called CLASS (Canadian Land Surface Scheme), as embedded in the MESH (Modélisation Environmentale Communautaire – Surface and Hydrology) modelling system, to (1) characterize the effect of soil profile depth under different climate conditions and in the presence of parameter uncertainty; (2) assess the effect of including or excluding the geothermal flux in the LSM at the bottom of the soil column; and (3) develop a methodology for temperature profile initialization in permafrost regions, where the system has an extended memory, by the use of paleo-records and bootstrapping. Our study area is in Norman Wells, Northwest Territories of Canada, where measurements of soil temperature profiles and historical reconstructed climate data are available. Our results demonstrate a dominant role for parameter uncertainty, that is often neglected in LSMs. Considering such high sensitivity to parameter values and dependency on the climate condition, we show that a minimum depth of 20 m is essential to adequately represent the temperature dynamics. We further show that our proposed initialization procedure is effective and robust to uncertainty in paleo-climate reconstructions and that more than 300 years of reconstructed climate time series are needed for proper model initialization.

Abstract. Drought is a recurring extreme climate event and among the most costly natural disasters in the world. This is particularly true over Canada, where drought is both a frequent and damaging phenomenon with impacts on regional water resources, agriculture, industry, aquatic ecosystems and health. However, nation-wide drought assessments are currently lacking and impacted by limited ground-based observations. This study provides a comprehensive analysis of historical droughts over the whole of Canada, including the role of large-scale teleconnections. Drought events are characterized by the Standardized Precipitation-Evapotranspiration Index (SPEI) over various temporal scales (1, 3, 6, and 12 consecutive months, 6 months from April to September, and 12 months from October to September) applied to different gridded monthly data sets for the period 1950–2013. The Mann Kendall test, Rotated Empirical Orthogonal Function, Continuous Wavelet Transform, and Wavelet Coherence analyses are used, respectively, to investigate the trend, spatiotemporal patterns, periodicity, and teleconnectivity of drought events. Results indicate that southern (northern) parts of the country experienced significant trends towards drier (wetter) conditions although substantial variability exists. Two spatially well-defined regions with different temporal evolution of droughts were identified―the Canadian Prairies and Northern-central Canada. The analyses also revealed the presence of a dominant periodicity of between 8–32 months in the Prairie region, and 8–40 months in the Northern central region. These cycles of low-frequency variability are found to be associated principally to the Pacific-North American (PNA) and Multivariate El Niño/Southern Oscillation Index (MEI) relative to other considered large-scale climate indices. This study is the first of its kind to identify dominant periodicities in drought variability over the whole of Canada in terms of when the drought events occur, the duration, and how often they do so.

Abstract Hysteresis is a widely reported phenomenon in natural and engineered systems across different temporal and spatial scales. Its definition is non-unique and rather context-dependent, while systems with hysteretic behavior, including hydrological systems, are commonly referred to as path-dependent systems or systems with memory. Despite widespread existence of hysteretic processes, the current generation of hydrologic models do not directly account for hysteresis. In this paper, we review the fundamentals, theories, and general properties of hysteresis in the broad scientific literature and then focus on its representations in hydrological sciences. Through illustrative examples, we show how an incomplete understanding or representation of the underlying processes in a system can lead to considering the system as being path-dependent. We argue that, in most cases, hysteresis is a manifestation of our dimensionality-reducing approach to process understanding and representation. We further explain that modelling hysteresis in an ideal world requires a full-dimensional process representation, based on a perfect understanding of the processes, their heterogeneity, and their spatio-temporal scale dependency. We discuss, however, that the missing dimensions/physics in a hydrologic model may be compensated to some extent by enabling the model with formal hysteretic components. Moreover, we show that the conventional model structure and parameterization may be designed in a way to partially reproduce a desired hysteretic behavior.

This paper investigates the problem of global sensitivity analysis (GSA) of Dynamical Earth System Models and proposes a basis for how such analyses should be performed. We argue that (a) performance metric‐based approaches to parameter GSA are actually identifiability analyses, (b) the use of a performance metric to assess sensitivity unavoidably distorts the information provided by the model about relative parameter importance, and (c) it is a serious conceptual flaw to interpret the results of such an analysis as being consistent and accurate indications of the sensitivity of the model response to parameter perturbations. Further, because such approaches depend on availability of system state/output observational data, the analysis they provide is necessarily incomplete. Here we frame the GSA problem from first principles, using trajectories of the partial derivatives of model outputs with respect to controlling factors as the theoretical basis for sensitivity, and construct a global sensitivity matrix from which statistical indices of total period time‐aggregate parameter importance, and time series of time‐varying parameter importance, can be inferred. We demonstrate this framework using the HBV‐SASK conceptual hydrologic model applied to the Oldman basin in Canada and show that it disagrees with performance metric‐based methods regarding which parameters exert the strongest controls on model behavior. Further, it is highly efficient, requiring less than 1,000 base samples to obtain stable and robust parameter importance assessments for our 10‐parameter example.

Abstract Prewhitening, the process of eliminating or reducing short-term stochastic persistence to enable detection of deterministic change, has been extensively applied to time series analysis of a range of geophysical variables. Despite the controversy around its utility, methodologies for prewhitening time series continue to be a critical feature of a variety of analyses including: trend detection of hydroclimatic variables and reconstruction of climate and/or hydrology through proxy records such as tree rings. With a focus on the latter, this paper presents a generalized approach to exploring the impact of a wide range of stochastic structures of short- and long-term persistence on the variability of hydroclimatic time series. Through this approach, we examine the impact of prewhitening on the inferred variability of time series across time scales. We document how a focus on prewhitened, residual time series can be misleading, as it can drastically distort (or remove) the structure of variability across time scales. Through examples with actual data, we show how such loss of information in prewhitened time series of tree rings (so-called “residual chronologies”) can lead to the underestimation of extreme conditions in climate and hydrology, particularly droughts, reconstructed for centuries preceding the historical period.

Anonymous review of scientific manuscripts was intended to encourage reviewers to speak freely, but other models may be better for accountability and inclusivity.

Abstract The Global Precipitation Measurement (GPM) mission offers new opportunities for modeling a range of physical/hydrological processes at higher resolutions, especially for remote river systems where the hydrometeorological monitoring network is sparse and weather radar is not readily available. In this study, the recently released Integrated Multisatellite Retrievals for GPM [version 03 (V03) IMERG Final Run] product with high spatiotemporal resolution of 0.1° and 30 min is evaluated against ground-based reference measurements (at the 6-hourly, daily, and monthly time scales) over different terrestrial ecozones of southern Canada within a 23-month period from 12 March 2014 to 31 January 2016. While IMERG and ground-based observations show similar regional variations of mean daily precipitation, IMERG tends to overestimate higher monthly precipitation amounts over the Pacific Maritime ecozone. Results from using continuous as well as categorical skill metrics reveal that IMERG shows more satisfactory agreement at the daily and the 6-hourly time scales for the months of June–September, unlike November–March. In terms of precipitation extremes (defined by the 75th percentile threshold for reference data), apart from a tendency toward overdetection of heavy precipitation events, IMERG captured well the distribution of heavy precipitation amounts and observed wet/dry spell length distributions over most ecozones. However, low skill was found over large portions of the Montane Cordillera ecozone and a few stations in the Prairie ecozone. This early study highlights a potential applicability of V03 IMERG Final Run as a reliable source of precipitation estimates in diverse water resources and hydrometeorological applications for different regions in southern Canada.

This study proposes an integrated modeling system consisting of the physically-based MIKE SHE/MIKE 11 model, a cellular automata model, and general circulation models (GCMs) scenarios to investigate the independent and combined effects of future climate and land-use/land-cover (LULC) changes on the hydrology of a river system. The integrated modelling system is applied to the Elbow River watershed in southern Alberta, Canada in conjunction with extreme GCM scenarios and two LULC change scenarios in the 2020s and 2050s. Results reveal that LULC change substantially modifies the river flow regime in the east sub-catchment, where rapid urbanization is occurring. It is also shown that the change in LULC causes an increase in peak flows in both the 2020s and 2050s. The impacts of climate and LULC change on streamflow are positively correlated in winter and spring, which intensifies their influence and leads to a significant rise in streamflow, and, subsequently, increases the vulnerability of the watershed to spring floods. This study highlights the importance of using an integrated modeling approach to investigate both the independent and combined impacts of climate and LULC changes on the future of hydrology to improve our understanding of how watersheds will respond to climate and LULC changes.

Abstract This paper investigates the commonly overlooked “sensitivity” of sensitivity analysis (SA) to what we refer to as parameter “perturbation scale”, which can be defined as a prescribed size of the sensitivity-related neighbourhood around any point in the parameter space (analogous to step size Δ x for numerical estimation of derivatives). We discuss that perturbation scale is inherent to any (local and global) SA approach, and explain how derivative-based SA approaches (e.g., method of Morris) focus on small-scale perturbations, while variance-based approaches (e.g., method of Sobol) focus on large-scale perturbations. We employ a novel variogram-based approach, called Variogram Analysis of Response Surfaces (VARS), which bridges derivative- and variance-based approaches. Our analyses with different real-world environmental models demonstrate significant implications of subjectivity in the perturbation-scale choice and the need for strategies to address these implications. It is further shown how VARS can uniquely characterize the perturbation-scale dependency and generate sensitivity measures that encompass all sensitivity-related information across the full spectrum of perturbation scales.

Complex hydrological models are being increasingly used nowadays for many purposes such as studying the impact of climate and land-use change on water resources. However, building a high-fidelity model, particularly at large scales, remains a challenging task, due to complexities in model functioning and behavior and uncertainties in model structure, parameterization, and data. Global Sensitivity Analysis (GSA), which characterizes how the variation in the model response is attributed to variations in its input factors (e.g., parameters, forcing data), provides an opportunity to enhance the development and application of these complex models. In this paper, we advocate using GSA as an integral part of the modelling process by discussing its capabilities as a tool for diagnosing model structure and detecting potential defects, identifying influential factors, characterizing uncertainty, and selecting calibration parameters. Accordingly, we conduct a comprehensive GSA of a complex land surface-hydrology model, Modelisation Environmentale–Surface et Hydrologie (MESH), which combines the Canadian Land Surface Scheme (CLASS) with a hydrological routing component, WATROUTE. Various GSA experiments are carried out using a new technique, called Variogram Analysis of Response Surfaces (VARS), for alternative hydroclimatic conditions in Canada using multiple criteria, various model configurations, and a full set of model parameters. Results from this study reveal that, in addition to different hydroclimatic conditions and SA criteria, model configurations can also have a major impact on the assessment of sensitivity. GSA can identify aspects of the model internal functioning that are counter-intuitive, and thus, help the modeler to diagnose possible model deficiencies and make recommendations for improving development and application of the model. As a specific outcome of this work, a list of the most influential parameters for the MESH model is developed. This list, along with some specific recommendations, is expected to assist the wide community of MESH and CLASS users, to enhance their modelling applications.

Efficient sampling strategies that scale with the size of the problem, computational budget, and users needs are essential for various sampling-based analyses, such as sensitivity and uncertainty analysis. In this study, we propose a new strategy, called Progressive Latin Hypercube Sampling (PLHS), which sequentially generates sample points while progressively preserving the distributional properties of interest (Latin hypercube properties, space-filling, etc.), as the sample size grows. Unlike Latin hypercube sampling, PLHS generates a series of smaller sub-sets (slices) such that (1) the first slice is Latin hypercube, (2) the progressive union of slices remains Latin hypercube and achieves maximum stratification in any one-dimensional projection, and as such (3) the entire sample set is Latin hypercube. The performance of PLHS is compared with benchmark sampling strategies across multiple case studies for Monte Carlo simulation, sensitivity and uncertainty analysis. Our results indicate that PLHS leads to improved efficiency, convergence, and robustness of sampling-based analyses. A new sequential sampling strategy called PLHS is proposed for sampling-based analysis of simulation models.PLHS is evaluated across multiple case studies for Monte Carlo simulation, sensitivity and uncertainty analysis.PLHS provides better performance compared with the other sampling strategies in terms of convergence rate and robustness.PLHS can be used to monitor the performance of the associated sampling-based analysis and to avoid over- or under-sampling.

AbstractThe high impact of river ice phenomena on the hydrology of cold regions has led to the extensive use of numerical models in simulating and predicting river ice processes. Consequently, ther...

Abstract. A number of global and regional gridded climate products based on multiple data sources are available that can potentially provide reliable estimates of precipitation for climate and hydrological studies. However, research into the consistency of these products for various regions has been limited and in many cases non-existent. This study inter-compares several gridded precipitation products over 15 terrestrial ecozones in Canada for different seasons. The spatial and temporal variability of the errors (relative to station observations) was quantified over the period of 1979 to 2012 at a 0.5° and daily spatio-temporal resolution. These datasets were assessed in their ability to represent the daily variability of precipitation amounts by four performance measures: percentage of bias, root mean square error, correlation coefficient, and standard deviation ratio. Results showed that most of the datasets were relatively skilful in central Canada. However, they tended to overestimate precipitation amounts in the west and underestimate in the north and east, with the underestimation being particularly dominant in northern Canada (above 60° N). The global product by WATCH Forcing Data ERA-Interim (WFDEI) augmented by Global Precipitation Climatology Centre (GPCC) data (WFDEI [GPCC]) performed best with respect to different metrics. The Canadian Precipitation Analysis (CaPA) product performed comparably with WFDEI [GPCC]; however, it only provides data starting in 2002. All the datasets performed best in summer, followed by autumn, spring, and winter in order of decreasing quality. Findings from this study can provide guidance to potential users regarding the performance of different precipitation products for a range of geographical regions and time periods.

Hydrologic model development and calibration have continued in most cases to focus only on accurately reproducing streamflows. However, complex models, for example, the so-called physically based models, possess large degrees of freedom that, if not constrained properly, may lead to poor model performance when used for prediction. We argue that constraining a model to represent streamflow, which is an integrated resultant of many factors across the watershed, is necessary but by no means sufficient to develop a high-fidelity model. To address this problem, we develop a framework to utilize the Gravity Recovery and Climate Experiment's (GRACE) total water storage anomaly data as a supplement to streamflows for model calibration, in a multiobjective setting. The VARS method (Variogram Analysis of Response Surfaces) for global sensitivity analysis is used to understand the model behaviour with respect to streamflow and GRACE data, and the BORG multiobjective optimization method is applied for model calibration. Two subbasins of the Saskatchewan River Basin in Western Canada are used as a case study. Results show that the developed framework is superior to the conventional approach of calibration only to streamflows, even when multiple streamflow-based error functions are simultaneously minimized. It is shown that a range of (possibly false) system trajectories in state variable space can lead to similar (acceptable) model responses. This observation has significant implications for land-surface and hydrologic model development and, if not addressed properly, may undermine the credibility of the model in prediction. The framework effectively constrains the model behaviour (by constraining posterior parameter space) and results in more credible representation of hydrology across the watershed.